In particular, there are two challenges in deriving the certified intersection size. The first challenge is that the base multi-label classifier predicts multiple labels for an input. The second challenge is that an input has multiple ground truth labels. To solve the first challenge, we propose a variant of Neyman-Pearson Lemma [1]} that is applicable to multiple functions, which correspond to multiple labels predicted by the base multi-label classifier. In contrast, existing randomized smoothing studies [2]}, [3]}, [4]}, [5]} for multi-class classification use the standard Neyman-Pearson Lemma [1]} that is only applicable for a single function, since their base multi-class classifier predicts a single label for an input. To address the second challenge, we propose to use the law of contraposition to simultaneously consider multiple ground truth labels of an input when deriving the certified intersection size.
